Directed Graph Research Articles

Graph total variation and low-rank regularization for heterogeneous change detection

Heterogeneous change detection (HCD) is challenging because different imaging mechanisms for various sensors make images difficult to compare directly. To address this problem, a graph-based regression algorithm is proposed for HCD, by leveraging the Graph Total Variation regularization and Low-Rank matrices decomposition (GTVLR). Utilizing graph signal processing (GSP) theory, a directed graph (digraph) model is employed to effectively represent the orientation and correlation information of images, thereby enabling direct comparison of heterogeneous data within the same domain after graph filtering. The GTVLR framework facilitates the decomposition of post-event images into regression and changed images. This decomposition ensures that the regression image mirrors the structure similarity of the pre-event image, while the changed image highlights areas of alteration, aiding in change detection. The model characterizes the piecewise smoothness and Low-Rank properties of data through GTV regularization and Low-Rank penalty, respectively. Moreover, by integrating the higher-order neighboring information within the digraph to refine the model. Experiments conducted on three real-world datasets and comparison with several state-of-the-art methods demonstrate the effectiveness of the proposed algorithm.

Approximation of subgraph counts in the uniform attachment model

Abstract We use Stein’s method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and multi-variate Poisson approximations to the counts of cycles and normal approximations to the counts of unicyclic subgraphs; we also give a partial result for the counts of trees. We further find a class of multicyclic graphs whose subgraph counts are a.s. bounded as $n\to \infty$ .

A Fast Algorithm for All-Pairs-Shortest-Paths Suitable for Neural Networks.

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: if the edges are given by the adjacency matrix Aij, then with a suitably small value of γ, the shortest path distances are Dij=ceil(logγ[(I-γA)-1]ij).We derive several graph-theoretic bounds on the value of γ and explore its useful range with numerics on different graph types. Even when the distance function is not globally accurate across the entire graph, it still works locally to instruct pursuit of the shortest path. In this mode, it also extends to weighted graphs with positive edge weights. For a wide range of dense graphs, this distance function is computationally faster than the best available alternative. Finally, we show that this method leads naturally to a neural network solution of the all-pairs-shortest-path problem.

Inverse system based decoupling design and control strategy for crude oil heat exchanger networks

This work focuses on a decoupling control approach for the crude oil heat exchanger network to improve the energy efficiency and achieve continuous energy saving. The desired control variables are identified by the signed directed graph (SDG) model based on the complex network theory. Then the principal component analysis (PCA) method and the evaluation index are employed to construct the initial controller as well as the control variables pairing. The presented system is a multi-input multi-output (MIMO) control system where the coupling problems are considered, and a decoupling control strategy based on the inverse system theory of neural network is proposed. The existence of the inverse system is proved by the reversibility derivation, and the original system is decoupled into two second-order subsystems. Consequently, the proposed decoupling control system is tested on the example of heat exchanger network (HEN) belonging to Crude Distillation Unit. The fluctuating value of temperature is reduced averagely by 57.1% compared with the non-decoupling control strategy and the mean absolute percentage error is within 0.02 under different operating conditions. The results show that the proposed decoupling control method has excellent decoupling performance and can improve the control performance of the system.

On network deconvolution for undirected graphs.

Network deconvolution (ND) is a method to reconstruct a direct-effect network describing direct (or conditional) effects (or associations) between any two nodes from a given network depicting total (or marginal) effects (or associations). Its key idea is that, in a directed graph, a total effect can be decomposed into the sum of a direct and an indirect effects, with the latter further decomposed as the sum of various products of direct effects. This yields a simple closed-form solution for the direct-effect network, facilitating its important applications to distinguish direct and indirect effects. Despite its application to undirected graphs, it is not well known why the method works, leaving it with skepticism. We first clarify the implicit linear model assumption underlying ND, then derive a surprisingly simple result on the equivalence between ND and use of precision matrices, offering insightful justification and interpretation for the application of ND to undirected graphs. We also establish a formal result to characterize the effect of scaling a total-effect graph. Finally, leveraging large-scale genome-wide association study data, we show a novel application of ND to contrast marginal versus conditional genetic correlations between body height and risk of coronary artery disease; the results align with an inferred causal directed graph using ND. We conclude that ND is a promising approach with its easy and wide applicability to both directed and undirected graphs.

Redicolouring digraphs: Directed treewidth and cycle-degeneracy

Given a digraph D=(V,A) on n vertices and a vertex v∈V, the cycle-degree of v is the minimum size of a set S⊆V(D)∖{v} intersecting every directed cycle of D containing v. From this definition of cycle-degree, we define the c-degeneracy (or cycle-degeneracy) of D, which we denote by δc∗(D). It appears to be a nice generalisation of the undirected degeneracy. For instance, the dichromatic number χ→(D) of D is bounded above by δc∗(D)+1, where χ→(D) is the minimum integer k such that D admits a k-dicolouring, i.e., a partition of its vertices into k acyclic subdigraphs.In this work, using this new definition of cycle-degeneracy, we extend several evidences for Cereceda’s conjecture (Cereceda, 2007) to digraphs. The k-dicolouring graph of D, denoted by Dk(D), is the undirected graph whose vertices are the k-dicolourings of D and in which two k-dicolourings are adjacent if they differ on the colour of exactly one vertex. This is a generalisation of the k-colouring graph of an undirected graph G, in which the vertices are the proper k-colourings of G.We show that Dk(D) has diameter at most Oδc∗(D)(nδc∗(D)+1) (respectively O(n2) and (δc∗(D)+1)n) when k is at least δc∗(D)+2 (respectively 32(δc∗(D)+1) and 2(δc∗(D)+1)). This improves known results on digraph redicolouring (Bousquet et al., 2023). Next, we extend a result due to Feghali (2021) to digraphs, showing that Dd+1(D) has diameter at most Od,ϵ(n(logn)d−1) when D has maximum average cycle-degree at most d−ϵ.We then show that two proofs of Bonamy and Bousquet (2018) for undirected graphs can be extended to digraphs. The first one uses the digrundy number of a digraph χ→g(D), which is the worst number of colours used in a greedy dicolouring. If k≥χ→g(D)+1, we show that Dk(D) has diameter at most 4⋅χ→(D)⋅n. The second one uses the D-width of a digraph, denoted by Dw(D), which is a generalisation of the treewidth to digraphs. If k≥Dw(D)+2, we show that Dk(D) has diameter at most 2(n2+n).Finally, we give a general theorem which makes a connection between the recolourability of a digraph D and the recolourability of its underlying graph UG(D). Assume that G is a class of undirected graphs, closed under edge-deletion and with bounded chromatic number, and let k≥χ(G) (i.e., k≥χ(G) for every G∈G) be such that, for every n-vertex graph G∈G, the diameter of the k-colouring graph of G is bounded by f(n) for some function f. We show that, for every n-vertex digraph D such that UG(D)∈G, the diameter of Dk(D) is bounded by 2f(n). For instance, this result directly extends a number of results on planar graph recolouring to planar digraph redicolouring.

Meeting, coalescence and consensus time on random directed graphs

Meeting, coalescence and consensus time on random directed graphs

A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction.

In this article, we consider the problem of inferring the sign of a link based on known sign data in signed networks. Regarding this link sign prediction problem, signed directed graph neural networks (SDGNNs) provides the best prediction performance currently to the best of our knowledge. In this article, we propose a different link sign prediction architecture called subgraph encoding via linear optimization (SELO), which obtains overall leading prediction performances compared to the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization (LO) method. Comprehensive experiments are conducted on five real-world signed networks with area under curve (AUC), F1, micro-F1, and macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the five real-world networks and in all the four evaluation metrics.

The λ -fold Spectrum Problem for the Orientations of the 6-Cycle

The λ-fold complete symmetric directed graph of order v, denoted λKv*, is the directed graph on v vertices and λ directed edges in each direction between each pair of vertices. For a given directed graph D, the set of all v for which λKv* admits a D-decomposition is called the λ-fold spectrum of D. In this paper, we settle the λ-fold spectrum of each of the nine non-isomorphic orientations of a 6-cycle.

Some Results Concerning Directed Graphs Over Commutative Rings

This paper delves into the idea of a directed graph that presented and illustrated, A directed graph for every finite, commutative ring is presented in this paper by utilizing the additive and multiplicative properties. This is achieved based on the mapping (a, b) → (a + b, a • b). The essential objective of this research work is to examine the characteristics of these directed graphs, specifically the valuable information they offer about the ring itself. To this end, we have adopted and presented several theorems and Corollaries with their proofs to support the obtained results

Extraction of logical networks during decompiling transistor-level CMOS circuit descriptions

Objectives. The problem of restoring the functional description of digital VLSI devices presented at the transistor level is considered. The objective of the work is to develop means for extraction of blocks representing logical networks from two-level descriptions of CMOS circuits at the transistor level, which were obtained as a result of recognition (extraction) of subcircuits that implement logic elements.Methods. Graph based methods and software tools are proposed for extracting a connected blocks representing a logical network from two-level descriptions of a transistor circuits in SPICE format. In the graph interpretation, the task is reduced to constructing a labeled directed graph of a logical network based on a labeled undirected bipartite graph specifying a two-level description of the transistor circuit.Results. The proposed method makes it possible to identify lexicographically ranked logical networks, from which a transition is made to logical equations that specify the functions implemented at the outputs of the resulting networks. Software tools have been developed that provide the generation of a hierarchical description in SPICE format that implements the original circuit at the transistor level, as well as descriptions of found logical networks in the SF language of hierarchical structural and functional descriptions of discrete devices and in high-level languages (VHDL and Verilog).Conclusion. The developed methods are implemented in C++, included in the program for decompiling transistor CMOS circuits and tested within it on practical examples of transistor-level circuits. The paper provides examples of reverse engineering of some practical transistor circuits.

Multi-view learning framework for predicting unknown types of cancer markers via directed graph neural networks fitting regulatory networks.

The discovery of diagnostic and therapeutic biomarkers for complex diseases, especially cancer, has always been a central and long-term challenge in molecular association prediction research, offering promising avenues for advancing the understanding of complex diseases. To this end, researchers have developed various network-based prediction techniques targeting specific molecular associations. However, limitations imposed by reductionism and network representation learning have led existing studies to narrowly focus on high prediction efficiency within single association type, thereby glossing over the discovery of unknown types of associations. Additionally, effectively utilizing network structure to fit the interaction properties of regulatory networks and combining specific case biomarker validations remains an unresolved issue in cancer biomarker prediction methods. To overcome these limitations, we propose a multi-view learning framework, CeRVE, based on directed graph neural networks (DGNN) for predicting unknown type cancer biomarkers. CeRVE effectively extracts and integrates subgraph information through multi-view feature learning. Subsequently, CeRVE utilizes DGNN to simulate the entire regulatory network, propagating node attribute features and extracting various interaction relationships between molecules. Furthermore, CeRVE constructed a comparative analysis matrix of three cancers and adjacent normal tissues through The Cancer Genome Atlas and identified multiple types of potential cancer biomarkers through differential expression analysis of mRNA, microRNA, and long noncoding RNA. Computational testing of multiple types of biomarkers for 72 cancers demonstrates that CeRVE exhibits superior performance in cancer biomarker prediction, providing a powerful tool and insightful approach for AI-assisted disease biomarker discovery.

Multi-Behavior Recommendation with Personalized Directed Acyclic Behavior Graphs

A well-developed recommendation system can not only leverage multi-typed interactions (such as page view, add-to-cart, and purchase) to better identify user preferences, but also demonstrate high performance, low complexity, and strong interpretability. However, many existing solutions for multi-behavior recommendation fall short of intuitive modeling of real-world scenarios, leading to overly complex models with massive parameters and cumbersome components. In particular, they share two critical limitations: (1) Some pioneering models are built upon the strict assumption of cascade effects across behaviors, which contradicts multifarious behavior paths in practical applications. (2) Existing approaches fail to explicitly capture the unique idiosyncrasies of users and even neglect the inherent nature of items involved in the multi-behavior interactions. To this end, we propose a novel Directed Acyclic Graph Convolutional Network (DA-GCN) for the multi-behavior recommendation task. Specifically, we pinpoint the partial order relations within the monotonic behavior chain and extend it to personalized directed acyclic behavior graphs to exploit behavior dependencies. Then, a GCN-based directed edge encoder is employed to distill rich collaborative signals embodied by each directed edge. In light of the information flows over the directed acyclic structure, we propose an attentive aggregation module to gather messages from all potential antecedent behaviors, representing distinct perspectives to understand the terminated behavior. Thus, we obtain comprehensive representations for the follow-up behavior through learnable distributions over its preceding behaviors, explicitly reflecting personalized interactive patterns of users and underlying properties of items simultaneously. Finally, we design a customized multi-task learning objective for flexible joint optimization. Extensive experiments on public benchmarking datasets fully demonstrate the superiority of DA-GCN with significant performance improvement and computational efficiency over a wide range of state-of-the-art methods. Our code is available at https://github.com/xizhu1022/DA-GCN .

Research on pure azimuth passive positioning of unmanned aerial vehicle formation in electromagnetic silence environment

In the electromagnetic silence environment, for the azimuth-only passive localization problem in the conical formation, it was concluded that there was a deviation between the ideal standard formation and the actual formation. These disturbance deviations should be eliminated to make the UAV reach the ideal formation state. Therefore, the adjustment model of individual UAV, the directed graph model of formation node and the MDP model of adjustment strategy are constructed. Based on the relevant factor model constructed, the azimuth-only passive localization model in conical formation is established and solved in MATLAB. Finally, experiments and analysis are carried out in the simulation environment, and the effectiveness and feasibility of the proposed algorithm are proved.

Copula Approximate Bayesian Computation Using Distribution Random Forests

Ongoing modern computational advancements continue to make it easier to collect increasingly large and complex datasets, which can often only be realistically analyzed using models defined by intractable likelihood functions. This Stats invited feature article introduces and provides an extensive simulation study of a new approximate Bayesian computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, that unifies and extends previous ABC methods proposed separately. This framework, copulaABCdrf, aims to accurately estimate and describe the possibly skewed and high-dimensional posterior distribution by a novel multivariate copula-based meta-t distribution based on univariate marginal posterior distributions that can be accurately estimated by distribution random forests (drf), while performing automatic summary statistics (covariates) selection, based on robustly estimated copula dependence parameters. The copulaABCdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of the ABC framework is illustrated and compared with previous standard ABC methods through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. This paper also proposes and studies a new solution to the simulation cost problem in ABC involving the posterior estimation of parameters from datasets simulated from the given model that are smaller compared to the potentially large size of the dataset being analyzed. This proposal is motivated by the fact that, for many models defined by intractable likelihoods, such as the network models when they are applied to analyze massive networks, the repeated simulation of large datasets (networks) for posterior-based parameter estimation can be too computationally costly and vastly slow down or prohibit the use of standard ABC methods. The copulaABCdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks of sizes ranging between 28,000 and 65.6 million nodes (between 3 million and 1.8 billion edges), including a large multilayer network with weighted directed edges. The results of the simulation studies show that, in settings where the true posterior distribution is not highly multimodal, copulaABCdrf usually produced similar point estimates from the posterior distribution for low-dimensional parametric models as previous ABC methods, but the copula-based method can produce more accurate estimates from the posterior distribution for high-dimensional models, and, in both dimensionality cases, usually produced more accurate estimates of univariate marginal posterior distributions of parameters. Also, posterior estimation accuracy was usually improved when pre-selecting the important summary statistics using drf compared to ABC employing no pre-selection of the subset of important summaries. For all ABC methods studied, accurate estimation of a highly multimodal posterior distribution was challenging. In light of the results of all the simulation studies, this article concludes by discussing how the copulaABCdrf framework can be improved for future research.

Incorporating hydrological constraints with deep learning for streamflow prediction

Streamflow prediction is a fundamental task serving for flood prevention and efficient water resource management. Deep learning-based methods have emerged as the dominant approach and have made remarkable progress in the task. However, these methods ignore the hydrological constraints on streamflow, such as water delay time and streamflow direction, resulting in inaccurate prediction. To address this problem, this study incorporates hydrological constraints with deep learning models to improve streamflow prediction, and develops a hydrological constrained graph convolutional network (HCGCN) model. Specifically, the model designs a time-delayed spatiotemporal directed graph to present the spatiotemporal relationships and hydrological constraints, and develops a hydrological feature aggregation module to adaptively learn the complex spatiotemporal dependencies. In addition, HCGCN proposes a streamflow prediction neural network to predict streamflow by stacking the feature aggregation modules. Experimental results show that HCGCN significantly improves the prediction accuracy in a real streamflow prediction task. This study provides an exploration of introducing hydrological constraints to improve streamflow prediction, and provides a new reference for various hydrological prediction tasks.

Homophily-Enhanced Self-Supervision for Graph Structure Learning: Insights and Directions.

Graph neural networks (GNNs) have recently achieved remarkable success on a variety of graph-related tasks, while such success relies heavily on a given graph structure that may not always be available in real-world applications. To address this problem, graph structure learning (GSL) is emerging as a promising research topic where task-specific graph structure and GNN parameters are jointly learned in an end-to-end unified framework. Despite their great progress, existing approaches mostly focus on the design of similarity metrics or graph construction, but directly default to adopting downstream objectives as supervision, which lacks deep insight into the power of supervision signals. More importantly, these approaches struggle to explain how GSL helps GNNs, and when and why this help fails. In this article, we conduct a systematic experimental evaluation to reveal that GSL and GNNs enjoy consistent optimization goals in terms of improving the graph homophily. Furthermore, we demonstrate theoretically and experimentally that task-specific downstream supervision may be insufficient to support the learning of both graph structure and GNN parameters, especially when the labeled data are extremely limited. Therefore, as a complement to downstream supervision, we propose homophily-enhanced self-supervision for GSL (HES-GSL), a method that provides more supervision for learning an underlying graph structure. A comprehensive experimental study demonstrates that HES-GSL scales well to various datasets and outperforms other leading methods. Our code will be available in https://github.com/LirongWu/Homophily-Enhanced-Self-supervision.

Resilient Neuroadaptive Distributed Fixed-Time Attitude Coordination Control for Multiple Spacecraft.

This work studies the attitude coordination tracking problem for multiple spacecraft with consideration of unintended faults (communication link faults and actuator faults), inertial uncertainties, and external disturbances under a directed communication graph. A resilient neuroadaptive distributed fixed-time control scheme is investigated to solve this challenging problem. First, an improved adaptive distributed observer is established for followers to estimate the states of the leader when considering communication link faults. The proposed observer improves the resilience against communication link faults. Subsequently, to further cope with the problem of actuator faults, inertial uncertainties, and external disturbances, based on the proposed observer and the technique of adding a power integrator, a neuroadaptive distributed fixed-time attitude coordination controller is developed. Unlike the existing controllers, the proposed one requires less information when dealing with faults and lumped uncertainties, and has a lower-computational cost. Moreover, the fixed-time stability of the closed-loop system is ensured under the designed resilient neuroadaptive distributed control scheme. Finally, comparative simulations are carried out to manifest the effectiveness of the investigated coordination control method.

Equivalent conditions for the synchronization of identical linear systems over arbitrary interconnections

We propose necessary and sufficient conditions for the synchronization of N identical single-input–single-output (SISO) systems, connected through a directed graph without imposing any assumption on the graph interconnection. We consider both the continuous-time and the discrete-time case, and we provide conditions that are equivalent to the uniform global exponential stability, with guaranteed convergence rate, of the closed and unbounded attractor that corresponds to the synchronization set.

Missile Fault Detection and Localization Based on HBOS and Hierarchical Signed Directed Graph

The rudder surfaces and lifting surfaces of a missile are utilized to acquire aerodynamic forces and moments, adjust the missile’s attitude, and achieve precise strike missions. However, the harsh flying conditions of missiles make the rudder surfaces and lifting surfaces susceptible to faults. In practical scenarios, there is often a scarcity of fault data, and sometimes, it is even difficult to obtain such data. Currently, data-driven fault detection and localization methods heavily rely on fault data, posing challenges for their applicability. To address this issue, this paper proposes an HBOS (Histogram-Based Outlier Score) online fault-detection method based on statistical distribution. This method generates a fault-detection model by fitting the probability distribution of normal data and incorporates an adaptive threshold to achieve real-time fault detection. Furthermore, this paper abstracts the interrelationships between the missile’s flight states and the propagation mechanism of faults into a hierarchical directed graph model. By utilizing bilateral adaptive thresholds, it captures the first fault features of each sub-node and determines the fault propagation effectiveness of each layer node based on the compatibility path principle, thus establishing a fault inference and localization model. The results of semi-physical simulation experiments demonstrate that the proposed algorithm is independent of fault data and exhibits high real-time performance. In multiple sets of simulated tests with randomly parameterized deviations, the fault-detection accuracy exceeds 98% with a false-alarm rate of no more than 0.31%. The fault-localization algorithm achieves an accuracy rate of no less than 97.91%.